Finally we note that thm:robust-corradi-hajnal is not the first result establishing a robust version of the Hajnal–Szemerédi theorem. The counting statement in thm:robust-corradi-hajnal generalizes a result of Sárközy, Selkow, and Szemerédi [1]}, where they proved that a Dirac-graph with has at least \((cn)^{n/2}\)  perfect matchings for a small constant \(c\) . We note that the optimal constant \(c\)  (which is achieved by the random graph of the appropriate density) was proven by Cuckler and Kahn [2]}; the extension of such a result to \(K_r\) -factors would be of substantial interest. Second, a resilience version of the Corrádi–Hajnal theorem [3]} (which is the \(r=3\)  case of the Hajnal–Szemerédi theorem) was proven by Balogh, Lee, and Samotij [4]}: with high probability \(\mathbb {G}(n,p)\)  with \(p=\omega ((\log n/n)^{1/2})\)  is such that every subgraph with minimum degree \((2/3+o(1))np\)  contains a triangle factor covering all but \(O(p^{-2})\)  vertices. This theorem is optimal both with the range of \(p\)  and the size of the exceptional set of vertices.
